Time and Energy Complexity of Distributed Computation of a Class of Functions in Wireless Sensor Networks

We consider a scenario in which a wireless sensor network is formed by randomly deploying n sensors to measure some spatial function over a field, with the objective of computing a function of the measurements and communicating it to an operator station. We restrict ourselves to the class of type-threshold functions (as defined in the work of Giridhar and Kumar, 2005), of which max, min, and indicator functions are important examples: our discussions are couched in terms of the max function. We view the problem as one of message-passing distributed computation over a geometric random graph. The network is assumed to be synchronous, and the sensors synchronously measure values and then collaborate to compute and deliver the function computed with these values to the operator station. Computation algorithms differ in (1) the communication topology assumed and (2) the messages that the nodes need to exchange in order to carry out the computation. The focus of our paper is to establish (in probability) scaling laws for the time and energy complexity of the distributed function computation over random wireless networks, under the assumption of centralized contention-free scheduling of packet transmissions. First, without any constraint on the computation algorithm, we establish scaling laws for the computation time and energy expenditure for one-time maximum computation. We show that for an optimal algorithm, the computation time and energy expenditure scale, respectively, as Theta(radicn/log n) and Theta(n) asymptotically as the number of sensors n rarr infin. Second, we analyze the performance of three specific computation algorithms that may be used in specific practical situations, namely, the tree algorithm, multihop transmission, and the Ripple algorithm (a type of gossip algorithm), and obtain scaling laws for the computation time and energy expenditure as n rarr infin. In particular, we show that the computation time for these algorithms scales as Theta(radicn/lo- g n), Theta(n), and Theta(radicn log n), respectively, whereas the energy expended scales as , Theta(n), Theta(radicn/log n), and Theta(radicn log n), respectively. Finally, simulation results are provided to show that our analysis indeed captures the correct scaling. The simulations also yield estimates of the constant multipliers in the scaling laws. Our analyses throughout assume a centralized optimal scheduler, and hence, our results can be viewed as providing bounds for the performance with practical distributed schedulers.

Rendering stiffer walls: a hybrid haptic system using continuous and discrete time feedback

Instability in conventional haptic rendering destroys the perception of rigid objects in virtual environments. Inherent limitations in the conventional haptic loop restrict the maximum stiffness that can be rendered. In this paper we present a method to render virtual walls that are much stiffer than those achieved by conventional techniques. By removing the conventional digital haptic loop and replacing it with a part-continuous and part-discrete time hybrid haptic loop, we were able to render stiffer walls. The control loop is implemented as a combinational logic circuit on an field-programmable gate array. We compared the performance of the conventional haptic loop and our hybrid haptic loop on the same haptic device, and present mathematical analysis to show the limit of stability of our device. Our hybrid method removes the computer-intensive haptic loop from the CPU-this can free a significant amount of resources that can be used for other purposes such as graphical rendering and physics modeling. It is our hope that, in the future, similar designs will lead to a haptics processing unit (HPU).

Application of D transforms in the analysis of nonlinear distributed parameter systems

The scope of application of Laplace transforms presently limited to the study of linear partial differential equations, is extended to the nonlinear domain by this study. This has been achieved by modifying the definition of D transforms, put forth recently for the study of classes of nonlinear lumped parameter systems. The appropriate properties of the new D transforms are presented to bring out their applicability in the analysis of nonlinear distributed parameter systems.

Equivalence conditions for classes of linear and non-linear distributed parameter systems

Equivalence of certain classes of second-order non-linear distributed parameter systems and corresponding linear third-order systems is established through a differential transformation technique. As linear systems are amenable to analysis through existing techniques, this study is expected to offer a method of tackling certain classes of non-linear problems which may otherwise prove to be formidable in nature.

Improved Conditions For L2-Stability Of Nonstationary Feedback-Systems

Concerning the L2-stability of feedback systems containing a linear time-varying operator, some of the stringent restrictions imposed on the multiplier as well as the linear part of the system, in the criteria presented earlier, are relaxed.

Time-Domain Criteria For L2-Stability Of Nonstationary Feedback-Systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

Low Power continuous time common mode sensing for common mode feedback circuits

Continuous common mode feedback (CMFB) circuits having high input impedance and low distortion are proposed. The proposed circuits are characterized for 0.18 mu m CMOS process with 1.8 V supply. Simulation results indicate that the proposed common mode detector consumes no standby power and CMFB circuit consumes 27-34% less power than previous high swing CMFB circuits.

A non-orthogonal distributed space-time coded protocol - Part 1:Signal model and design criteria

In this two-part series of papers, a generalized non-orthogonal amplify and forward (GNAF) protocol which generalizes several known cooperative diversity protocols is proposed. Transmission in the GNAF protocol comprises of two phases - the broadcast phase and the cooperation phase. In the broadcast phase, the source broadcasts its information to the relays as well as the destination. In the cooperation phase, the source and the relays together transmit a space-time code in a distributed fashion. The GNAF protocol relaxes the constraints imposed by the protocol of Jing and Hassibi on the code structure. In Part-I of this paper, a code design criteria is obtained and it is shown that the GNAF protocol is delay efficient and coding gain efficient as well. Moreover GNAF protocol enables the use of sphere decoders at the destination with a non-exponential Maximum likelihood (ML) decoding complexity. In Part-II, several low decoding complexity code constructions are studied and a lower bound on the Diversity-Multiplexing Gain tradeoff of the GNAF protocol is obtained.

Distributed space-time codes with reduced decoding complexity

We address the problem of distributed space-time coding with reduced decoding complexity for wireless relay network. The transmission protocol follows a two-hop model wherein the source transmits a vector in the first hop and in the second hop the relays transmit a vector, which is a transformation of the received vector by a relay-specific unitary transformation. Design criteria is derived for this system model and codes are proposed that achieve full diversity. For a fixed number of relay nodes, the general system model considered in this paper admits code constructions with lower decoding complexity compared to codes based on some earlier system models.

An efficient and scalable checkpointing and recovery algorithm for distributed systems

In this paper, we describe an efficient coordinated-checkpointing and recovery algorithm which can work even when the channels are assumed to be non-FIFO, and messages may be lost. Nodes are assumed to be autonomous, and they do not block while taking checkpoints. Based on the local conditions, any process can request the previous coordinator for the 'permission' to initiate a new checkpoint. Allowing multiple initiators of checkpoints avoids the bottleneck associated with a single initiator, but the algorithm permits only a single instance of checkpointing process at any given time, thus reducing much of the overhead associated with multiple initiators of distributed algorithms.

Framework for enabling highly available distributed applications for utility computing

The move towards IT outsourcing is the first step towards an environment where compute infrastructure is treated as a service. In utility computing this IT service has to honor Service Level Agreements (SLA) in order to meet the desired Quality of Service (QoS) guarantees. Such an environment requires reliable services in order to maximize the utilization of the resources and to decrease the Total Cost of Ownership (TCO). Such reliability cannot come at the cost of resource duplication, since it increases the TCO of the data center and hence the cost per compute unit. We, in this paper, look into aspects of projecting impact of hardware failures on the SLAs and techniques required to take proactive recovery steps in case of a predicted failure. By maintaining health vectors of all hardware and system resources, we predict the failure probability of resources based on observed hardware errors/failure events, at runtime. This inturn influences an availability aware middleware to take proactive action (even before the application is affected in case the system and the application have low recoverability). The proposed framework has been prototyped on a system running HP-UX. Our offline analysis of the prediction system on hardware error logs indicate no more than 10% false positives. This work to the best of our knowledge is the first of its kind to perform an end-to-end analysis of the impact of a hardware fault on application SLAs, in a live system.

A neural network based CBIR system using STI features and relevance feedback

Multimedia mining primarily involves, information analysis and retrieval based on implicit knowledge. The ever increasing digital image databases on the Internet has created a need for using multimedia mining on these databases for effective and efficient retrieval of images. Contents of an image can be expressed in different features such as Shape, Texture and Intensity-distribution(STI). Content Based Image Retrieval(CBIR) is an efficient retrieval of relevant images from large databases based on features extracted from the image. Most of the existing systems either concentrate on a single representation of all features or linear combination of these features. The paper proposes a CBIR System named STIRF (Shape, Texture, Intensity-distribution with Relevance Feedback) that uses a neural network for nonlinear combination of the heterogenous STI features. Further the system is self-adaptable to different applications and users based upon relevance feedback. Prior to retrieval of relevant images, each feature is first clustered independent of the other in its own space and this helps in matching of similar images. Testing the system on a database of images with varied contents and intensive backgrounds showed good results with most relevant images being retrieved for a image query. The system showed better and more robust performance compared to existing CBIR systems

Robust multivariable controllers for a tublar ammonia reactor

The specific objective of this paper is to develop multivariable controllers that would achieve asymptotic regulation in the presence of parameter variations and disturbance inputs for a tubular reactor used in ammonia synthesis. A ninth order state space model with three control inputs and two disturbance inputs is generated from the nonlinear distributed model using linearization and lumping approximations. Using this model, an approach for control system design is developed keeping in view the imperfections of the model and the measurability of the state variables. Specifically, the design of feedforward and robust integral controllers using state and output feedback is considered. Also, the design of robust multiloop proportional integral controllers is presented. Finally the performance of these controllers is evaluated through simulation.

Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A sub-space based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.

Distributed Transmission of Functions of Correlated Sources over a Fading Multiple Access Channel

In this paper we address the problem of distributed transmission of functions of correlated sources over a fast fading multiple access channel (MAC). This is a basic building block in a hierarchical sensor network used in estimating a random field where the cluster head is interested only in estimating a function of the observations. The observations are transmitted to the cluster head through a fast fading MAC. We provide sufficient conditions for lossy transmission when the encoders and decoders are provided with partial information about the channel state. Furthermore signal side information maybe available at the encoders and the decoder. Various previous studies are shown as special cases. Efficient joint-source channel coding schemes are discussed for transmission of discrete and continuous alphabet sources to recover function values.